A recent asymptotics-based thermomechanical model is adapted and applied to the mould region in the continuous casting of round steel billets, with a view to describing the complex interplay between air-gap formation, mould taper, cooling channel width and cooling water velocity. Although the situation is steady state, the analysis leads to what is mathematically a dual moving-boundary problem for the solid–melt and solid–air interfaces, where the distance from the top of the mould region is the time-like variable in the problem. Moreover, the two interfaces are initiated at different locations. In addition, the thermal and mechanical problems are found to decouple and it is possible to solve the first ahead of the second. The model equations are solved numerically using a finite-difference method, and the approach is subsequently successfully validated against a previous finite-element model and experimental data from temperature measurements taken within the mould.

中文翻译：

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一种经过验证的钢连铸锥形结晶器气隙形成的渐近热机械模型

最近基于渐近的热机械模型被改编并应用于圆钢坯连铸的结晶器区域，以描述气隙形成、结晶器锥度、冷却通道宽度和冷却水速度之间的复杂相互作用。虽然情况是稳定的，但分析导致固-熔和固-气界面在数学上是一个双重移动边界问题，其中距模具区域顶部的距离是问题中的类时间变量. 此外，这两个接口在不同的位置启动。此外，发现热和机械问题可以解耦，可以先解决第一个问题。使用有限差分法对模型方程进行数值求解，